Opposed to the alpha versions I’ve seen, the video quality is very good and the Flash player does not cause any problems under GNU/Linux (I tested it on the latest version of Adobe Flash on Ubuntu 7.10 Gutsy Gibbon running Firefox and GNOME),
The only thing that the Linux version does not support is the possibility to download the video. This is due to DRM technology used to prevent storing the files for more than 7 days.
BBC Player -- main window
TV programme for today
Watching BBC World News
Unfortunately, the BBC iPlayer is currently available only to the British citizens (i.e. people connecting to the Intertent from IP addresses recognized as British). I don’t know of any plans to make the service available to other countries/whole world.
You can browse the BBC iPlayer programs on the official iPlayer website.